On a phase transition model of Penrose-Fife type

Gianni Gilardi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 3-4, page 169-181
  • ISSN: 1120-6330

Abstract

top
We deal with a Penrose-Fife type model for phase transition. We assume a rather general constitutive low for the heat flux and treat the Dirichlet and Neumann boundary condition for the temperature. Some of our proofs apply to different types of boundary conditions as well and improve some results existing in the literature.

How to cite

top

Gilardi, Gianni. "On a phase transition model of Penrose-Fife type." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 15.3-4 (2004): 169-181. <http://eudml.org/doc/252294>.

@article{Gilardi2004,
abstract = {We deal with a Penrose-Fife type model for phase transition. We assume a rather general constitutive low for the heat flux and treat the Dirichlet and Neumann boundary condition for the temperature. Some of our proofs apply to different types of boundary conditions as well and improve some results existing in the literature.},
author = {Gilardi, Gianni},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Phase transition; Penrose-Fife model; Heat flux law; Boundary conditions; Well-posedness},
language = {eng},
month = {12},
number = {3-4},
pages = {169-181},
publisher = {Accademia Nazionale dei Lincei},
title = {On a phase transition model of Penrose-Fife type},
url = {http://eudml.org/doc/252294},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Gilardi, Gianni
TI - On a phase transition model of Penrose-Fife type
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/12//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 3-4
SP - 169
EP - 181
AB - We deal with a Penrose-Fife type model for phase transition. We assume a rather general constitutive low for the heat flux and treat the Dirichlet and Neumann boundary condition for the temperature. Some of our proofs apply to different types of boundary conditions as well and improve some results existing in the literature.
LA - eng
KW - Phase transition; Penrose-Fife model; Heat flux law; Boundary conditions; Well-posedness
UR - http://eudml.org/doc/252294
ER -

References

top
  1. BROKATE, M. - SPREKELS, J., Hysteresis and phase transitions. Springer-Verlag, NewYork1996. Zbl0951.74002MR1411908DOI10.1007/978-1-4612-4048-8
  2. COLLI, P. - GILARDI, G. - ROCCA, E. - SCHIMPERNA, G., On a Penrose-Fife phase field model with inhomogeneous Neumann boundary condition for the temperature. Preprint IAN-CNR n. 1327, 2003, 1-21. Zbl1224.35222MR2054932
  3. COLLI, P. - LAURENÇOT, PH., Weak solutions to the Penrose-Fife phase field model for a class of admissible flux laws. Physica D, vol. 111, 1998, 311-334. Zbl0929.35062MR1601442DOI10.1016/S0167-2789(97)80018-8
  4. COLLI, P. - LAURENÇOT, PH. - SPREKELS, J., Global solution to the Penrose-Fife phase field model with special heat flux laws. In: P. ARGOUL - M. FRÉMOND - Q.S. NGUYEN (eds.), Variations of Domains and Free-Boundary Problems in Solid Mechanics. Solid Mech. Appl., 66, Kluwer Acad. Publ., Dordrecht1999, 181-188. MR1672241DOI10.1007/978-94-011-4738-5_21
  5. COLLI, P. - SPREKELS, J., On a Penrose-Fife model with zero interfacial energy leading to a phase-field system of relaxed Stefan type. Ann. Mat. Pura Appl., vol. 169, 1995, 269-289. Zbl0852.35030MR1378478DOI10.1007/BF01759357
  6. GILARDI, G. - MARSON, A., On a Penrose-Fife type system with Dirichlet boundary conditions for the temperature. Math. Methods Appl. Sci., 26, 2003, 1303-1325. Zbl1029.82014MR2004103DOI10.1002/mma.423
  7. HORN, W. - LAURENÇOT, PH. - SPREKELS, J., Global solutions to a Penrose-Fife phase-field model under flux boundary conditions for the inverse temperature. Math. Methods Appl. Sci., vol. 19, 1996, 1053-1072. Zbl0859.35049MR1402815DOI10.1002/(SICI)1099-1476(19960910)19:13<1053::AID-MMA809>3.0.CO;2-S
  8. HORN, W. - SPREKELS, J. - ZHENG, S., Global existence for the Penrose-Fife phase-field model of Ising ferromagnets. Adv Math. Sci. Appl., vol. 6, 1996, 227-241. Zbl0858.35053MR1385769
  9. KENMOCHI, N. - KUBO, M., Weak solutions of nonlinear systems for non-isothermal phase transitions. Adv Math. Sci. Appl., vol. 9, 1999, 499-521. Zbl0930.35037MR1690439
  10. KENMOCHI, N. - NIEZGÓDKA, M., Evolution equations of nonlinear variational inequalities arising from phase change problems. Nonlinear Analysis, TMA, vol. 22, 1994, 1163-1180. Zbl0827.35070MR1279139DOI10.1016/0362-546X(94)90235-6
  11. KENMOCHI, N. - NIEZGÓDKA, M., Systems of nonlinear parabolic equations for phase change problems. Adv Math. Sci. Appl., vol. 3, 1993/94, 89-117. Zbl0827.35015
  12. LAURENÇOT, PH., Solutions to a Penrose-Fife model of phase field type. J. Math. Anal. Appl., vol. 185, 1994, 262-274. Zbl0819.35159MR1283056DOI10.1006/jmaa.1994.1247
  13. LAURENÇOT, PH., Weak solutions to a Penrose-Fife model for phase transitions. Adv Math. Sci. Appl., vol. 5, 1995, 117-138. Zbl0829.35148MR1325962
  14. LAURENÇOT, PH., Weak solutions to a Penrose-Fife model with Fourier law for the temperature. J. Math. Anal. Appl., vol. 219, 1998, 331-343. Zbl0919.35137MR1606330DOI10.1006/jmaa.1997.5813
  15. PENROSE, O. - FIFE, P.C., Thermodinamically consistent models of phase field type for the kinetics of phase-transitions. Physica D, vol. 43, 1990, 44-62. Zbl0709.76001MR1060043DOI10.1016/0167-2789(90)90015-H
  16. SPREKELS, J. - ZHENG, S., Global smooth solutions to a thermodynamically consistent model of phase field type in higher space dimensions. J. Math. Anal. Appl., vol. 176, 1993, 200-223. Zbl0804.35063MR1222165DOI10.1006/jmaa.1993.1209
  17. VISINTIN, A., Models of phase transitions. Progress in Nonlinear Differential Equations, vol. 28, Birkhäuser, Boston1996. Zbl0882.35004MR1423808DOI10.1007/978-1-4612-4078-5
  18. ZHENG, S., Global smooth solutions to a thermodynamically consistent model of phase field type. Diff. Integral Eqns., vol. 5, 1992, 241-253. Zbl0768.35050

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.